We discuss ongoing studies of a sample of E+A galaxies that are largely optically quiet but for which radio data demonstrate, or strongly indicate, the presence of a low-luminosity buried AGN. Conventionally, radio emission in E+A galaxies is used as a measure of current, possibly optically obscured, star formation. However, recent VLA observations show that several of our objects contain confirmed, or highly likely, variable radio point sources and/or large scale extended radio lobes reminiscent of powerful radio galaxies. Many of these E+A galaxies show morphological evidence of mergers or significant interactions. Has the AGN lasted at a low luminosity since the previous major epoch of star formation > 100 Myr years ago, or have smaller-scale and more recent star formation episodes occurred which might have reenergized the central black hole? To investigate the potential connection between AGN activity and star formation history in these galaxies, we are pursuing a vigorous observing campaign on the WIYN telescope including deep optical spectra obtained with the Sparsepak IFU and near infrared images from WHIRC. For example, a combination of deep exposures and wide spectral coverage will allow us to trace the age and metallicity history of the stars in different parts of these galaxies since the beginning of the merger/major interaction.